Summary: ARTICLE Communicated by Carlos Brody
Sampling Properties of the Spectrum and Coherency of
Sequences of Action Potentials
M. R. Jarvis
Division of Biology, California Institute of Technology, Pasadena, California 91125,
U.S.A.
P. P. Mitra
Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974, U.S.A.
The spectrum and coherency are useful quantities for characterizing the
temporal correlations and functional relations within and between point
processes. This article begins with a review of these quantities, their
interpretation, and how they may be estimated. A discussion of how
to assess the statistical significance of features in these measures is in-
cluded. In addition, new work is presented that builds on the framework
established in the review section. This work investigates how the es-
timates and their error bars are modified by finite sample sizes. Finite
sample corrections are derived based on a doubly stochastic inhomoge-
neous Poisson process model in which the rate functions are drawn from
a low-variance gaussian process. It is found that in contrast to continuous
processes, the variance of the estimators cannot be reduced by smooth-